That link is somewhat useful but clearly the modulation scheme (1 is in a 2 mS window, 0 is in a 1mS window) isn't used by your remote. One thing that does seem interesting is the fact that they transmit the inverted signal after 40 mS. Are you seeing anything like that?
I would be tempted to hook directly to the emitter on the remote control to eliminate your receiver as a source of the variability. It will probably give you the same results but worth eliminating every possible source of error.
I wonder if there is some sort of rolling code or sequence that the remote goes through. I'd write some specialized code to look for the common lead-in sequence and then only spit out the variable part at the end as a hex or binary code. This would allow more efficient experimentation. If it's a rolling code thing, there will be a point where it repeat since there aren't that many bits. The last bit or bits of each sequence might be some sort of check digit (parity or whatever). Also, I'd see what happens if you let the remote sit unused for a while, do you get the same sequence?